Best Answer

Interior angle 156 degrees

Exterior angle 24 degrees

360/24 = 15 sides

Q: In a regular polygon the ratio of an exterior angle to the measure of an interior angle is 2 to13 how many sides does the polygon have?

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The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=15, then the answer is thatthe interior angle = 12x13 =156The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 15, then the answer is that the exterior angle = 24

The largest exterior angle measure is 120o. It is the exterior measure of an equilateral triangle (which is a regular polygon).

It has 32 sides and each interior angle measures 168.75 degrees and so 180-168.75 = 11.25 degrees which is the measure of each exterior angle

This is not possible for a normal regular polygon. (A regular polygon has all equal angles and all equal sides. A normal polygon has no intersecting edges.)The smallest regular polygon is an equilateral triangle (a three sided polygon), whose exterior angle measure is twice the measure of its interior angle. A four-sided polygon (a square) has equal interior and exterior angle measures of 90⁰. Starting from a five-sided polygon, the exterior angle measure is smaller than the interior angle measure.Let's assume that the given information is true. So we need to verify it.Let's say that the interior angle of the regular polygon has a measure of x degrees, and the measure of the exterior angle of that polygon is 4x degrees.Since the sum of the interior and the exterior angles of the polygon is 180 degrees (a straight line), the interior angle is 36 degrees.4x + x = 1805x = 1805x/5 = 180/5x = 36The sum of the angles of a polygon = 180⁰(n - 2), where n is the number of the sides of the polygon.The measure of one of the angles of a polygon = 180⁰(n - 2)/n. Substituting the angle measure of 36⁰ into this formula, we have:36⁰ = 180⁰(n - 2)/n (multiply by n to both sides)36⁰n = 180⁰(n - 2)36⁰n = 180⁰n - 360⁰ (add 360⁰ and subtract 36⁰n to both sides)360⁰ = 144⁰n (divide by 144⁰ to both sides)2.5 = n !!That means that a such normal polygon does not exist.

For regular polygons, all the interior angles are the same measure, while the sum of the exterior angles is always 360 for any regular polygon. Use these facts and the fact that each interior/exterior angle pair has a sum of 180 to answer this question. 360 divided by 8 = 45. So each exterior angle of the figure measures 45. 180 - 45 = 135, so each interior angle measures 135 degrees.

Related questions

It is: 180-exterior angle = interior angle because there are 180 degrees on a straight line

180

30 degrees

999999

That would depend on how many sides it has.

360

The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=9, then the answer is that the interior angle = 140The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 9, then the answer is that the exterior angle = 40

The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=18, then the answer is that the interior angle = 160The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 18, then the answer is that the exterior angle = 20

The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=10, then the answer is that the interior angle = 144The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 10, then the answer is that the exterior angle = 36

144o. Sum of exterior angles of a polygon is 360o. Each exterior angle for a regular decagon is 360o / 10 = 36o. Exterior and interior angles are supplementary, that is sum to 180o. Therefore the interior angle of a regular decagon is 180o - 36o = 144o.

Each exterior angle: 72 degrees Each interior angle: 108 degrees

The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=15, then the answer is thatthe interior angle = 12x13 =156The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 15, then the answer is that the exterior angle = 24